Cremona's table of elliptic curves

192 = 2⁶ · 3

Field	Data	Notes
Atkin-Lehner	2+ 3+	Signs for the Atkin-Lehner involutions
Class	192a	Isogeny class
Conductor	192	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	98304 = 215 · 3	Discriminant
Eigenvalues	2+ 3+ -2 -4 -4  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-129,609]	[a1,a2,a3,a4,a6]
Generators	[-11:24:1]	Generators of the group modulo torsion
j	7301384/3	j-invariant
L	1.1195591687307	L(r)(E,1)/r!
Ω	3.3132763404732	Real period
R	1.3516037344121	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	192b3 96a3 576c3 4800x3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 192a3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	+	-2	-4	-4	2	-6	4	0	-2	4	2	2	-4	8	-10	4	-6	-4	-16	-6	4	-12	10	-14

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Quadratic twists for elliptic curve 192a3

-4	8	-3	5	-7	-11	13	17	-19	-23
192b3	96a3	576c3	4800x3	9408bg3	23232u4	32448e4	55488bj4	69312bv4	101568k4

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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